Oh I'm sure they do, just like any other advanced society. Predators have creeds and codes and all that good stuff, so it only makes sense that some of these may conflict and spark wars.
"If anything in this life is certain, if history has taught us anything, it is that you can kill anyone." - Michael Corleone
They may simply unleash xenomorph on the opposing side..................
~For centuries, human beings have worshipped these beasts as gods, beasts that will forever haunt us, beasts waging an eternal war.....~ http://www.freewebs.com/shanezilla
I'm not so sure, but I say they do. And I agree with the two posts above mine. They could easily unleash Aliens on the opposing side, possibly some other thing like a Rancor or that ancient type of raptor Predator: Concrete Jungle says they were supposed to hunt. I think they would go to war, and probably even have a history of a few wars on their planet. Again, the way they are, they would at least have thought of starting a war...
*Sarcastic Voice*: To me, everyone is crazy. The ones in the Mental House just got caught.